Aperture fields of paraboloidal reflectors by stereographic mapping of feed polarization

For any paraboloidal reflector operating in a focused condition, the aperture-field orientation may be obtained by first stereographically mapping the feed-polarization pattern and then overlaying the paraboloid aperture on the projection. Examples shown are for electric and magnetic dipoles, and Huygens source feeds pointed at central and offset sections of the paraboloidal reflector.